Supplement: Distance vs. time. Articulatory and acoustic consequences of reduced vowel duration in Polish

Patrycja Strycharczuk, Małgorzata Ćavar, Stefano Coretta

1 Overview

This supplementary document complements the paper Distance vs. time. Articulatory and acoustic consequences of reduced vowel duration in Polish.

The following sections illustrate:

The articulatory data normalisation procedure.
Descriptive plots of the raw data.
Code and plots of the linear regression models.
Summaries of the models in 3.
Extra analyses of F0 and F3.

Only relevant R code is shown in this document. The full code can be inspected on the OSF repository at https://osf.io/hy7nt/?view_only=d06775a2cb1d4786a0442b0f15d73296, in the file code/analysis.Rmd.

2 Normalisation procedure

This is Figure 1 from the paper, which illustrates the normalisation procedure. See paper for details.

## The origin is x = 16.8107470216526, y = -50.1837719761868.

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3 Descriptive statistics plots

3.1 Articulatory undershoot

Tongue contours from ultrasound tongue imaging of speaker PL01. Tongue tip on the right.

## The origin is x = 16.8107470216526, y = -50.1837719761868.

## The origin is x = 16.8107470216526, y = -50.1837719761868.

3.2 Duration

Figure 2 from the paper with boxplots and means of vowel duration depending on speech rate and stress.

3.3 Vowel space

3.3.1 Acoustic vowel space

## `summarise()` has grouped output by 'V1'. You can override using the `.groups` argument.
## `summarise()` has grouped output by 'V1'. You can override using the `.groups` argument.

3.3.2 Articulatory vowel space

## `summarise()` has grouped output by 'V1'. You can override using the `.groups` argument.
## `summarise()` has grouped output by 'V1'. You can override using the `.groups` argument.

3.3.3 Save

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4 Inferential statistics

4.1 VIF (multicollinearity)

VIF values below 3 indicate absence of multicollinearity (Zuur, Ieno, and Elphick 2010). For all predictors, VIF < 3.

##   Variables      VIF
## 1  duration 2.169934
## 2      f1.z 1.379401
## 3      f2.z 1.208097
## 4      f0.z 1.122029
## 5      rate 1.639475
## 6    stress 1.451903

4.2 Duration

4.3 F1

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4.4 F2

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4.5 Z1

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4.6 Z2

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4.7 Composite plot

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5 Model summaries

5.1 Duration

	duration.log
Predictors	Estimates	CI	p
(Intercept)	3.77	3.63 – 3.91	<0.001
rate [normal]	0.19	0.09 – 0.30	<0.001
rate [slow]	0.45	0.31 – 0.59	<0.001
V11	0.00	-0.16 – 0.17	0.968
V12	-0.01	-0.16 – 0.14	0.913
V13	0.08	-0.08 – 0.25	0.333
V14	0.14	0.02 – 0.27	0.023
V15	0.00	-0.12 – 0.13	0.955
stress [stressed]	0.23	0.18 – 0.28	<0.001
rate [normal] * V11	0.05	-0.03 – 0.13	0.182
rate [slow] * V11	-0.02	-0.10 – 0.06	0.576
rate [normal] * V12	-0.01	-0.09 – 0.07	0.780
rate [slow] * V12	0.00	-0.08 – 0.08	0.960
rate [normal] * V13	0.01	-0.06 – 0.09	0.717
rate [slow] * V13	0.04	-0.04 – 0.12	0.339
rate [normal] * V14	-0.01	-0.09 – 0.07	0.786
rate [slow] * V14	-0.04	-0.12 – 0.03	0.268
rate [normal] * V15	-0.01	-0.08 – 0.07	0.901
rate [slow] * V15	0.02	-0.06 – 0.10	0.593
rate [normal] * stress [stressed]	0.15	0.10 – 0.20	<0.001
rate [slow] * stress [stressed]	0.18	0.13 – 0.23	<0.001
V11 * stress [stressed]	-0.07	-0.15 – 0.00	0.065
V12 * stress [stressed]	-0.05	-0.13 – 0.03	0.215
V13 * stress [stressed]	-0.02	-0.10 – 0.06	0.687
V14 * stress [stressed]	0.12	0.04 – 0.20	0.003
V15 * stress [stressed]	0.03	-0.05 – 0.11	0.473
(rate [normal] * V11) * stress [stressed]	-0.07	-0.18 – 0.04	0.209
(rate [slow] * V11) * stress [stressed]	-0.08	-0.19 – 0.03	0.173
(rate [normal] * V12) * stress [stressed]	-0.04	-0.15 – 0.07	0.465
(rate [slow] * V12) * stress [stressed]	-0.04	-0.16 – 0.07	0.455
(rate [normal] * V13) * stress [stressed]	0.02	-0.09 – 0.13	0.721
(rate [slow] * V13) * stress [stressed]	0.03	-0.08 – 0.14	0.621
(rate [normal] * V14) * stress [stressed]	-0.03	-0.14 – 0.09	0.655
(rate [slow] * V14) * stress [stressed]	-0.06	-0.17 – 0.06	0.331
(rate [normal] * V15) * stress [stressed]	0.00	-0.11 – 0.11	0.977
(rate [slow] * V15) * stress [stressed]	0.03	-0.08 – 0.15	0.555
Random Effects
σ²	0.04
τ₀₀ _frame	0.02
τ₀₀ _speaker	0.04
τ₁₁ _{speaker.ratenormal}	0.03
τ₁₁ _{speaker.rateslow}	0.05
τ₁₁ _{speaker.stressstressed}	0.00
ρ₀₁ _{speaker.ratenormal}	-0.81
ρ₀₁ _{speaker.rateslow}	-0.78
ρ₀₁ _{speaker.stressstressed}	-0.48
N _speaker	10
N _frame	12
Observations	1440
Marginal R² / Conditional R²	0.706 / NA

5.2 F1

	f1.z
Predictors	Estimates	CI	p
(Intercept)	-0.59	-0.78 – -0.41	<0.001
V11	-0.29	-0.69 – 0.12	0.163
V12	0.08	-0.29 – 0.46	0.660
V13	-0.00	-0.41 – 0.40	0.989
V14	0.38	0.04 – 0.72	0.029
V15	0.31	-0.02 – 0.64	0.064
duration	0.01	0.01 – 0.01	<0.001
stress [stressed]	0.40	0.24 – 0.56	<0.001
V11 * duration	-0.01	-0.01 – -0.01	<0.001
V12 * duration	-0.00	-0.00 – 0.00	0.710
V13 * duration	-0.01	-0.01 – -0.00	0.001
V14 * duration	0.02	0.01 – 0.02	<0.001
V15 * duration	-0.00	-0.01 – 0.00	0.180
V11 * stress [stressed]	-0.25	-0.55 – 0.05	0.100
V12 * stress [stressed]	-0.22	-0.54 – 0.09	0.165
V13 * stress [stressed]	-0.28	-0.59 – 0.03	0.077
V14 * stress [stressed]	0.41	0.06 – 0.76	0.022
V15 * stress [stressed]	0.16	-0.15 – 0.47	0.307
duration * stress [stressed]	-0.00	-0.01 – -0.00	0.005
(V11 * duration) * stress [stressed]	0.00	-0.00 – 0.01	0.608
(V12 * duration) * stress [stressed]	0.01	0.00 – 0.01	0.007
(V13 * duration) * stress [stressed]	0.00	-0.00 – 0.01	0.126
(V14 * duration) * stress [stressed]	-0.01	-0.01 – -0.00	0.024
(V15 * duration) * stress [stressed]	0.00	-0.00 – 0.01	0.692
Random Effects
σ²	0.17
τ₀₀ _frame	0.07
τ₀₀ _speaker	0.00
τ₁₁ _{speaker.stressstressed}	0.01
ρ₀₁ _speaker	-1.00
N _speaker	10
N _frame	12
Observations	1440
Marginal R² / Conditional R²	0.837 / NA

5.3 F2

	f2.z
Predictors	Estimates	CI	p
(Intercept)	-0.06	-0.24 – 0.13	0.550
V11	1.17	0.77 – 1.57	<0.001
V12	0.28	-0.08 – 0.63	0.132
V13	0.13	-0.27 – 0.53	0.531
V14	-0.38	-0.69 – -0.07	0.015
V15	-0.52	-0.82 – -0.22	0.001
duration	0.00	-0.00 – 0.00	0.283
stress [stressed]	0.05	-0.05 – 0.15	0.332
V11 * duration	0.01	0.00 – 0.01	<0.001
V12 * duration	0.00	-0.00 – 0.01	0.067
V13 * duration	0.00	-0.00 – 0.00	0.125
V14 * duration	0.00	-0.00 – 0.00	0.426
V15 * duration	-0.01	-0.01 – -0.00	<0.001
V11 * stress [stressed]	0.29	0.08 – 0.51	0.008
V12 * stress [stressed]	-0.02	-0.25 – 0.20	0.843
V13 * stress [stressed]	0.07	-0.15 – 0.29	0.519
V14 * stress [stressed]	0.04	-0.21 – 0.29	0.765
V15 * stress [stressed]	-0.12	-0.34 – 0.10	0.269
duration * stress [stressed]	-0.00	-0.00 – 0.00	0.600
(V11 * duration) * stress [stressed]	-0.00	-0.01 – 0.00	0.155
(V12 * duration) * stress [stressed]	0.00	-0.00 – 0.00	0.858
(V13 * duration) * stress [stressed]	0.00	-0.00 – 0.00	0.915
(V14 * duration) * stress [stressed]	-0.00	-0.00 – 0.00	0.630
(V15 * duration) * stress [stressed]	0.00	-0.00 – 0.00	0.382
Random Effects
σ²	0.09
τ₀₀ _frame	0.08
τ₀₀ _speaker	0.00
τ₁₁ _{speaker.stressstressed}	0.00
ρ₀₁ _speaker
N _speaker	10
N _frame	12
Observations	1440
Marginal R² / Conditional R²	0.908 / NA

5.4 Z1

	z1
Predictors	Estimates	CI	p
(Intercept)	-0.27	-0.41 – -0.13	<0.001
V11	-0.55	-0.85 – -0.26	<0.001
V12	-0.16	-0.44 – 0.12	0.256
V13	0.18	-0.12 – 0.48	0.240
V14	0.17	-0.09 – 0.43	0.211
V15	0.25	0.00 – 0.51	0.048
duration	0.00	0.00 – 0.01	<0.001
stress [stressed]	-0.02	-0.15 – 0.11	0.801
V11 * duration	-0.01	-0.01 – -0.00	0.001
V12 * duration	-0.00	-0.00 – 0.00	0.859
V13 * duration	-0.00	-0.01 – -0.00	0.003
V14 * duration	0.01	0.00 – 0.01	<0.001
V15 * duration	0.01	0.00 – 0.01	0.002
V11 * stress [stressed]	-0.09	-0.34 – 0.16	0.490
V12 * stress [stressed]	0.07	-0.19 – 0.33	0.591
V13 * stress [stressed]	-0.00	-0.26 – 0.25	0.988
V14 * stress [stressed]	-0.06	-0.35 – 0.23	0.697
V15 * stress [stressed]	0.03	-0.22 – 0.29	0.807
duration * stress [stressed]	-0.00	-0.00 – 0.00	0.619
(V11 * duration) * stress [stressed]	0.00	-0.00 – 0.00	0.544
(V12 * duration) * stress [stressed]	0.00	-0.00 – 0.00	0.952
(V13 * duration) * stress [stressed]	0.00	-0.00 – 0.00	0.803
(V14 * duration) * stress [stressed]	-0.00	-0.00 – 0.00	0.722
(V15 * duration) * stress [stressed]	0.00	-0.00 – 0.00	0.891
Random Effects
σ²	0.12
τ₀₀ _frame	0.03
τ₀₀ _speaker	0.00
τ₁₁ _{speaker.stressstressed}	0.01
ρ₀₁ _speaker	-1.00
N _speaker	10
N _frame	12
Observations	1440
Marginal R² / Conditional R²	0.734 / NA

5.5 Z2

	z2
Predictors	Estimates	CI	p
(Intercept)	0.13	-0.11 – 0.37	0.298
V11	1.09	0.57 – 1.62	<0.001
V12	0.33	-0.14 – 0.79	0.169
V13	-0.03	-0.56 – 0.50	0.912
V14	-0.27	-0.66 – 0.12	0.182
V15	-0.53	-0.92 – -0.15	0.007
duration	-0.00	-0.00 – -0.00	0.004
stress [stressed]	-0.04	-0.15 – 0.06	0.406
V11 * duration	0.00	0.00 – 0.01	0.002
V12 * duration	0.00	-0.00 – 0.00	0.607
V13 * duration	0.01	0.00 – 0.01	<0.001
V14 * duration	-0.00	-0.00 – 0.00	0.650
V15 * duration	-0.00	-0.01 – -0.00	0.005
V11 * stress [stressed]	0.02	-0.20 – 0.24	0.852
V12 * stress [stressed]	-0.09	-0.32 – 0.14	0.466
V13 * stress [stressed]	0.08	-0.15 – 0.31	0.506
V14 * stress [stressed]	0.09	-0.17 – 0.35	0.487
V15 * stress [stressed]	0.09	-0.14 – 0.31	0.457
duration * stress [stressed]	0.00	-0.00 – 0.00	0.270
(V11 * duration) * stress [stressed]	0.00	-0.00 – 0.00	0.658
(V12 * duration) * stress [stressed]	0.00	-0.00 – 0.00	0.779
(V13 * duration) * stress [stressed]	-0.00	-0.00 – 0.00	0.484
(V14 * duration) * stress [stressed]	-0.00	-0.01 – 0.00	0.326
(V15 * duration) * stress [stressed]	-0.00	-0.01 – 0.00	0.312
Random Effects
σ²	0.09
τ₀₀ _frame	0.15
τ₀₀ _speaker	0.00
τ₁₁ _{speaker.stressstressed}	0.00
ρ₀₁ _speaker
N _speaker	10
N _frame	12
Observations	1440
Marginal R² / Conditional R²	0.874 / NA

6 Further exploratory analyses

6.1 F0

## Linear mixed model fit by REML ['lmerMod']
## Formula: f0.z ~ (1 + stress | speaker) + (1 | frame) + V1 * duration *  
##     stress
##    Data: midpoint_rotated
## Control: 
## lmerControl(optimizer = "optimx", calc.derivs = FALSE, optCtrl = list(method = "bobyqa"))
## 
## REML criterion at convergence: 3391.2
## 
## Scaled residuals: 
##     Min      1Q  Median      3Q     Max 
## -2.7492 -0.6234 -0.0749  0.5778  4.9360 
## 
## Random effects:
##  Groups   Name           Variance Std.Dev. Corr 
##  frame    (Intercept)    0.02512  0.1585        
##  speaker  (Intercept)    0.24312  0.4931        
##           stressstressed 1.10736  1.0523   -1.00
##  Residual                0.54046  0.7352        
## Number of obs: 1436, groups:  frame, 12; speaker, 10
## 
## Fixed effects:
##                               Estimate Std. Error t value
## (Intercept)                 -0.9271354  0.1902833  -4.872
## V11                          0.0721928  0.2234686   0.323
## V12                         -0.2139909  0.2340587  -0.914
## V13                         -0.2441876  0.2317454  -1.054
## V14                          0.2990680  0.2423838   1.234
## V15                         -0.0418586  0.2258400  -0.185
## duration                     0.0126725  0.0017110   7.407
## stressstressed               0.8131770  0.3577448   2.273
## V11:duration                -0.0017780  0.0033075  -0.538
## V12:duration                 0.0009472  0.0037718   0.251
## V13:duration                 0.0015467  0.0032617   0.474
## V14:duration                -0.0103272  0.0036658  -2.817
## V15:duration                -0.0017363  0.0037012  -0.469
## V11:stressstressed          -0.2764102  0.2729397  -1.013
## V12:stressstressed           0.4183847  0.2846774   1.470
## V13:stressstressed          -0.1864312  0.2799947  -0.666
## V14:stressstressed          -0.2810617  0.3197088  -0.879
## V15:stressstressed           0.0117957  0.2794705   0.042
## duration:stressstressed     -0.0085098  0.0020061  -4.242
## V11:duration:stressstressed  0.0053459  0.0040823   1.310
## V12:duration:stressstressed -0.0075852  0.0044825  -1.692
## V13:duration:stressstressed  0.0033151  0.0038471   0.862
## V14:duration:stressstressed  0.0053035  0.0043042   1.232
## V15:duration:stressstressed  0.0003301  0.0042265   0.078

## 
## Correlation matrix not shown by default, as p = 24 > 12.
## Use print(x, correlation=TRUE)  or
##     vcov(x)        if you need it

## Warning in Analyze.model(focal.predictors, mod, xlevels, default.levels, : the
## predictor f0.z is a one-column matrix that was converted to a vector

## Warning: Removed 4 rows containing missing values (geom_point).

## Warning: Removed 4 rows containing missing values (geom_point).

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
## conversion failure on 'ɨ' in 'mbcsToSbcs': dot substituted for <c9>

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
## conversion failure on 'ɨ' in 'mbcsToSbcs': dot substituted for <a8>

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
## conversion failure on 'ɨ' in 'mbcsToSbcs': dot substituted for <c9>

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
## conversion failure on 'ɨ' in 'mbcsToSbcs': dot substituted for <a8>

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
## conversion failure on 'ɨ' in 'mbcsToSbcs': dot substituted for <c9>

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
## conversion failure on 'ɨ' in 'mbcsToSbcs': dot substituted for <a8>

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
## conversion failure on 'ɨ' in 'mbcsToSbcs': dot substituted for <c9>

## Warning in grid.Call(C_textBounds, as.graphicsAnnot(x$label), x$x, x$y, :
## conversion failure on 'ɨ' in 'mbcsToSbcs': dot substituted for <a8>

## Warning in grid.Call.graphics(C_text, as.graphicsAnnot(x$label), x$x, x$y, :
## conversion failure on 'ɨ' in 'mbcsToSbcs': dot substituted for <c9>

## Warning in grid.Call.graphics(C_text, as.graphicsAnnot(x$label), x$x, x$y, :
## conversion failure on 'ɨ' in 'mbcsToSbcs': dot substituted for <a8>

## Warning in grid.Call.graphics(C_text, as.graphicsAnnot(x$label), x$x, x$y, :
## conversion failure on 'ɨ' in 'mbcsToSbcs': dot substituted for <c9>

## Warning in grid.Call.graphics(C_text, as.graphicsAnnot(x$label), x$x, x$y, :
## conversion failure on 'ɨ' in 'mbcsToSbcs': dot substituted for <a8>

	f0.z
Predictors	Estimates	CI	p
(Intercept)	-0.93	-1.30 – -0.55	<0.001
V11	0.07	-0.37 – 0.51	0.747
V12	-0.21	-0.67 – 0.24	0.361
V13	-0.24	-0.70 – 0.21	0.292
V14	0.30	-0.18 – 0.77	0.217
V15	-0.04	-0.48 – 0.40	0.853
duration	0.01	0.01 – 0.02	<0.001
stress [stressed]	0.81	0.11 – 1.51	0.023
V11 * duration	-0.00	-0.01 – 0.00	0.591
V12 * duration	0.00	-0.01 – 0.01	0.802
V13 * duration	0.00	-0.00 – 0.01	0.635
V14 * duration	-0.01	-0.02 – -0.00	0.005
V15 * duration	-0.00	-0.01 – 0.01	0.639
V11 * stress [stressed]	-0.28	-0.81 – 0.26	0.311
V12 * stress [stressed]	0.42	-0.14 – 0.98	0.142
V13 * stress [stressed]	-0.19	-0.74 – 0.36	0.506
V14 * stress [stressed]	-0.28	-0.91 – 0.35	0.379
V15 * stress [stressed]	0.01	-0.54 – 0.56	0.966
duration * stress [stressed]	-0.01	-0.01 – -0.00	<0.001
(V11 * duration) * stress [stressed]	0.01	-0.00 – 0.01	0.190
(V12 * duration) * stress [stressed]	-0.01	-0.02 – 0.00	0.091
(V13 * duration) * stress [stressed]	0.00	-0.00 – 0.01	0.389
(V14 * duration) * stress [stressed]	0.01	-0.00 – 0.01	0.218
(V15 * duration) * stress [stressed]	0.00	-0.01 – 0.01	0.938
Random Effects
σ²	0.54
τ₀₀ _frame	0.03
τ₀₀ _speaker	0.24
τ₁₁ _{speaker.stressstressed}	1.11
ρ₀₁ _speaker	-1.00
N _speaker	10
N _frame	12
Observations	1436
Marginal R² / Conditional R²	0.257 / NA

6.2 F3

## `geom_smooth()` using formula 'y ~ x'

7 Session info

## ─ Session info ───────────────────────────────────────────────────────────────
##  setting  value                       
##  version  R version 4.0.3 (2020-10-10)
##  os       macOS Big Sur 10.16         
##  system   x86_64, darwin17.0          
##  ui       X11                         
##  language (EN)                        
##  collate  en_US.UTF-8                 
##  ctype    en_US.UTF-8                 
##  tz       Europe/Berlin               
##  date     2021-03-30                  
## 
## ─ Packages ───────────────────────────────────────────────────────────────────
##  ! package      * version    date       lib
##  P abind          1.4-5      2016-07-21 [?]
##  P assertthat     0.2.1      2019-03-21 [?]
##  P backports      1.2.1      2020-12-09 [?]
##  P bayestestR     0.8.2      2021-01-26 [?]
##  P bookdown       0.21       2020-10-13 [?]
##  P boot           1.3-27     2021-02-12 [?]
##  P broom          0.7.5      2021-02-19 [?]
##  P cachem         1.0.4      2021-02-13 [?]
##  P callr          3.5.1      2020-10-13 [?]
##  P car            3.0-10     2020-09-29 [?]
##  P carData      * 3.0-4      2020-05-22 [?]
##  P cellranger     1.1.0      2016-07-27 [?]
##  P cli            2.3.1      2021-02-23 [?]
##  P codetools      0.2-18     2020-11-04 [4]
##  P colorspace     2.0-0      2020-11-11 [?]
##  P cowplot        1.1.1      2020-12-30 [?]
##  P crayon         1.4.1      2021-02-08 [?]
##  P curl           4.3        2019-12-02 [?]
##  P data.table     1.14.0     2021-02-21 [?]
##  P DBI            1.1.1      2021-01-15 [?]
##  P dbplyr         2.1.0      2021-02-03 [?]
##  P desc           1.3.0      2021-03-05 [?]
##  P devtools       2.3.2      2020-09-18 [?]
##  P digest         0.6.27     2020-10-24 [?]
##  P dplyr        * 1.0.5      2021-03-05 [?]
##  P effects      * 4.2-0      2020-08-11 [?]
##  P effectsize     0.4.4      2021-03-14 [?]
##  P ellipsis       0.3.1      2020-05-15 [?]
##  P emmeans        1.5.5-1    2021-03-21 [?]
##  P estimability   1.3        2018-02-11 [?]
##  P evaluate       0.14       2019-05-28 [?]
##  P fansi          0.4.2      2021-01-15 [?]
##  P farver         2.1.0      2021-02-28 [?]
##  P fastmap        1.1.0      2021-01-25 [?]
##  P forcats      * 0.5.1      2021-01-27 [?]
##  P foreign        0.8-81     2020-12-22 [?]
##  P fs             1.5.0      2020-07-31 [?]
##  P generics       0.1.0      2020-10-31 [?]
##  P ggeffects      1.0.2      2021-03-17 [?]
##  P ggplot2      * 3.3.3      2020-12-30 [?]
##  P ggpubr       * 0.4.0      2020-06-27 [?]
##  P ggrepel      * 0.9.1      2021-01-15 [?]
##  P ggsignif       0.6.1      2021-02-23 [?]
##  P glue           1.4.2      2020-08-27 [?]
##  P gtable         0.3.0      2019-03-25 [?]
##  P haven          2.3.1      2020-06-01 [?]
##  P here           1.0.1      2020-12-13 [?]
##  P highr          0.8        2019-03-20 [?]
##  P hms            1.0.0      2021-01-13 [?]
##  P htmltools      0.5.1.1    2021-01-22 [?]
##  P httr           1.4.2      2020-07-20 [?]
##  P insight        0.13.1     2021-02-22 [?]
##  P jsonlite       1.7.2      2020-12-09 [?]
##  P knitr          1.31       2021-01-27 [?]
##  P labeling       0.4.2      2020-10-20 [?]
##  P lattice        0.20-41    2020-04-02 [4]
##  P lifecycle      1.0.0      2021-02-15 [?]
##  P lme4         * 1.1-26     2020-12-01 [?]
##  P lubridate      1.7.10     2021-02-26 [?]
##  P magrittr       2.0.1      2020-11-17 [?]
##  P MASS           7.3-53.1   2021-02-12 [?]
##  P Matrix       * 1.3-2      2021-01-06 [?]
##  P memoise        2.0.0      2021-01-26 [?]
##  P mgcv           1.8-34     2021-02-16 [?]
##  P minqa          1.2.4      2014-10-09 [?]
##  P mitools        2.4        2019-04-26 [?]
##  P modelr         0.1.8      2020-05-19 [?]
##  P munsell        0.5.0      2018-06-12 [?]
##  P mvtnorm        1.1-1      2020-06-09 [?]
##  P nlme           3.1-152    2021-02-04 [?]
##  P nloptr         1.2.2.2    2020-07-02 [?]
##  P nnet           7.3-15     2021-01-24 [?]
##  P numDeriv       2016.8-1.1 2019-06-06 [?]
##  P openxlsx       4.2.3      2020-10-27 [?]
##  P optimx       * 2020-4.2   2020-04-08 [?]
##  P parameters     0.12.0     2021-02-21 [?]
##  P performance  * 0.7.0      2021-02-03 [?]
##  P pillar         1.5.1      2021-03-05 [?]
##  P pkgbuild       1.2.0      2020-12-15 [?]
##  P pkgconfig      2.0.3      2019-09-22 [?]
##  P pkgload        1.2.0      2021-02-23 [?]
##  P prettyunits    1.1.1      2020-01-24 [?]
##  P processx       3.5.0      2021-03-23 [?]
##  P ps             1.6.0      2021-02-28 [?]
##  P purrr        * 0.3.4      2020-04-17 [?]
##  P R6             2.5.0      2020-10-28 [?]
##  P raster       * 3.4-5      2020-11-14 [?]
##  P Rcpp           1.0.6      2021-01-15 [?]
##  P readr        * 1.4.0      2020-10-05 [?]
##  P readxl         1.3.1      2019-03-13 [?]
##  P remotes        2.2.0      2020-07-21 [?]
##  P reprex         1.0.0      2021-01-27 [?]
##  P rio            0.5.26     2021-03-01 [?]
##  P rlang          0.4.10     2020-12-30 [?]
##  P rmarkdown      2.7        2021-02-19 [?]
##  P rmdformats     1.0.1      2021-01-13 [?]
##  P rprojroot      2.0.2      2020-11-15 [?]
##  P rstatix        0.7.0      2021-02-13 [?]
##  P rstudioapi     0.13       2020-11-12 [?]
##  P rticulate    * 1.6.0      2021-03-18 [?]
##  P rvest          1.0.0      2021-03-09 [?]
##  P scales         1.1.1      2020-05-11 [?]
##  P sessioninfo    1.1.1      2018-11-05 [?]
##  P sjlabelled     1.1.7      2020-09-24 [?]
##  P sjmisc         2.8.6      2021-01-07 [?]
##  P sjPlot       * 2.8.7      2021-01-10 [?]
##  P sjstats        0.18.1     2021-01-09 [?]
##  P sp           * 1.4-5      2021-01-10 [?]
##  P statmod        1.4.35     2020-10-19 [?]
##  P stringi        1.5.3      2020-09-09 [?]
##  P stringr      * 1.4.0      2019-02-10 [?]
##  P survey         4.0        2020-04-03 [?]
##  P survival       3.2-10     2021-03-16 [?]
##  P testthat       3.0.2      2021-02-14 [?]
##  P tibble       * 3.1.0      2021-02-25 [?]
##  P tidymv         3.2.0      2021-01-05 [?]
##  P tidyr        * 1.1.3      2021-03-03 [?]
##  P tidyselect     1.1.0      2020-05-11 [?]
##  P tidyverse    * 1.3.0      2019-11-21 [?]
##  P usdm         * 1.1-18     2017-06-25 [?]
##  P usethis        2.0.1      2021-02-10 [?]
##  P utf8           1.2.1      2021-03-12 [?]
##  P vctrs          0.3.6      2020-12-17 [?]
##  P withr          2.4.1      2021-01-26 [?]
##  P xfun           0.22       2021-03-11 [?]
##  P xml2           1.3.2      2020-04-23 [?]
##  P xtable         1.8-4      2019-04-21 [?]
##  P yaml           2.2.1      2020-02-01 [?]
##  P zip            2.1.1      2020-08-27 [?]
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## [1] /Users/ste/repos/polish-reduction/renv/library/R-4.0/x86_64-apple-darwin17.0
## [2] /private/var/folders/yj/b5zvw9lj2zg6tp920wyg14y80000gn/T/Rtmp8GVe2u/renv-system-library
## [3] /Library/Frameworks/R.framework/Versions/4.0/Resources/site-library
## [4] /Library/Frameworks/R.framework/Versions/4.0/Resources/library
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##  P ── Loaded and on-disk path mismatch.

Zuur, Alain F., Elena N. Ieno, and Chris S. Elphick. 2010. “A Protocol for Data Exploration to Avoid Common Statistical Problems.” Methods in Ecology and Evolution 1 (1): 3–14. https://doi.org/10.1111/j.2041-210X.2009.00001.x.